Course Topics
This course belongs to the type "Attività formative di base" and the subject area is "Matematica-Fisica". The aim of this course is to introduce the fundamental mathematical concepts and tools of differential and integral calculus, with a specific focus on their modeling applications in computer science. In particular, the course covers the elements of logic, set theory, and the principle of mathematical induction; the study of real functions of a single real variable (limits, continuity, and differential calculus) along with the geometric application of function graph analysis; local approximation via Taylor polynomials; the theory and convergence criteria of numerical series; Riemann integration and its extension to improper integrals.

Teaching format
The course includes frontal lectures and exercises.

Educational objectives
Knowledge and Understanding - D1.1: Have a solid knowledge of mathematical analysis, algebra, numerical calculus, discrete mathematics and elementary notion of logic that are in support of computer science Applying knowledge and understanding - D2.1: Be able to use the tools of mathematics and logic to solve problems. Ability to make judgments - D3.2: Be able to work autonomously according to the own level of knowledge and understanding. Communication skills - D4.1: Be able to use one of the three languages English, Italian and German, and be able to use technical terms and communication appropriately. Learning skills - D5.1: Have developed learning capabilities to pursue further studies with a high degree of autonomy.

Assessment
The written exam will include verification questions, transfer-of-knowledge questions, and exercises. The purpose of the assessment is to evaluate the extent to which students have achieved the learning outcomes related to knowledge and understanding, the application of knowledge, and the ability to make informed judgments. These criteria apply equally to both attending and non-attending students.

Evaluation criteria
The final written exam accounts for 100% of the final grade and covers the entire course program. Exam questions will be evaluated based on correctness, clarity, the quality of argumentation, and problem-solving ability. Students are offered a written midterm exam (held midway through the semester), which covers material from the first half of the course (to be specified in detail during the semester). The midterm accounts for 50% of the final exam grade. Students who fail the midterm or are unable to take it for any reason can take the final written exam instead. The midterm result is valid for three exam sessions.

Required readings

Canuto, C., Tabacco, A. Mathematical Analysis I, Springer.

Lecture Notes provided by the lecturer.

Supplementary readings

Adams, R. A., Essex, C. Calculus: A Complete Course (Chapters P–9), Pearson.

Any textbook of "Mathematical Analysis" or "Calculus".

Further information
If the use of specific software is required, it will be communicated during class by the lecturer.